Finite size scaling approach to Anderson localisation

Abstract

Using a new and powerful real space renormalisation method recently introduced for phase transitions, the authors prove numerically that two dimensions are marginal for Anderson localisation. An associated transition is found, presenting close analogies with the Kosterlitz-Thouless transition of the XY model in two dimensions, while the behaviour in three dimensions is shown to be a standard one with a mobility edge. The accuracy of the method is better than previous approaches in two dimensions and is not reduced when the number of dimensions is raised to three.